Log in

A differential geometric characterization of the first Painlevé transcendent

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Ablowitz, M., Ramani, A., Segur, H.: Nonlinear evolution equations and ordinary differential equations of the Painlevé type. Lett. Nuovo Cimento23, 33 (1978)

    Google Scholar 

  2. Bryant, R., Chern, S.S., Griffiths, P.A.: Exterior differential systems. Proceedings of the 1980 Bei**g Symposium on Differential Geometry and Differential Equations New York. Gordon and Breach 1982

  3. Cartan E.: Les sous — groupes des groupes continus de transformations. Ann. Ec. Norm25, 57 (1908). (Oeuvres Complètes Vol. 2, 719)

    Google Scholar 

  4. Gardner, R.B.: Differential geometric control theory. Brockett, R., Millman, R., Sussman, H. (Eds.) Progress in Mathematics 27. Basel, Boston, Stuttgart: Birkhäuser 1983

    Google Scholar 

  5. Ince, E.L.: Ordinary differential equations. New York, Dover 1956

    Google Scholar 

  6. Kamran, N., Lamb, K.G., Shadwick, W.F.: The local equivalence problem ford 2 y/dx 2 =F(x, y, dy/dx) and the Painlevé transcendents. J. Differ. Geom.22, 139 (1985)

    Google Scholar 

  7. Kamran, N., Shadwick, W.F.: The solution of the Cartan equivalence problem ford 2 y/dx 2 =F(x, y, dy/dx) under the pseudo-group 117. Lect. Notes Phys. 246, Sanchez, N. (Ed.) Berlin, Heidelberg, New York: Springer 1986

    Google Scholar 

  8. Painlevé, P.: Mémoire sur les équations différentielles dont l'intégrale générale est uniforme. Bull. Soc. Math. Fr.28, 2 (1900). (Oeuvres Complètes Vol. 3, 123)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported by grants from N.S.E.R.C.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kamran, N., Shadwick, W.F. A differential geometric characterization of the first Painlevé transcendent. Math. Ann. 279, 117–123 (1987). https://doi.org/10.1007/BF01456194

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01456194

Keywords

Navigation